The existence of quasi-periodic vortex patches close to the unit disc for the QGSW equations have been proved in [1]}. These solutions are obtained by selecting the Rossby deformation length in a massive Cantor set. Similarly, in [2]}, the authors used the parameter inside the equations to generate quasi-periodic vortex patches near the Rankine vortices for \((SQG)_{\alpha }\)  equations for suitable selected values of \(\alpha .\)  Here our work follows the same idea relying on the free parameter \(\alpha \)  to obtain these solutions. We mention two other works recently obtained for Euler equations. The first one concerns the quasi-periodic patches close to the Rankine vortices in the unit disc presented in [3]}. The second result, which can be found in [4]}, is relative to quasi-periodic patches close to the Kirchhoff ellipses. In both cases, this is a geometrical parameter which, when taken among a Cantor-like set of admissible parameters, allows to find quasi-periodic solutions. Our second result reads as follows.
